2520edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|2520}} | {{EDO intro|2520}} | ||
== Theory == | == Theory == | ||
2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors. | 2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors. | ||
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It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472. | It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472. | ||
2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[ | 2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[4225/4224]], [[4375/4374]], [[6656/6655]], {{monzo| -22 12 3 5 -2 -3 }}} and reaches the [[7/1|7th harmonic]] in 9 generators instead of 5. [[Eliora]] proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, {{monzo| -24 46 -15 0 -3 -1 }}}. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2520}} | {{Harmonics in equal|2520}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. | In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. | ||
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Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]). | Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]). | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
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| [[Barium]] | | [[Barium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||